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## Homework Statement

A mass M is split into two parts, m and M - m, which are then separated by a certain distance. What ratio m/M maximizes the magnitude of the gravitational force between the parts?

## Homework Equations

F=Gm1m2/d^2

## The Attempt at a Solution

I first just tried plugging in M - m and m in for m1 and m2 to see what I get.

F=(GMm-Gm)/d^2

I believe that I will have to take a derivative to find the maximum, but I am confused as to what I should take the derivative with respect to.